Special Issue on Traffic, Crowd, and SwarmsNo Access

VERTEX FLOW MODELS FOR VEHICULAR TRAFFIC ON NETWORKS

CIRO D'APICE

DIIMA, Universitá degli Studi di Salerno, Fisciano (SA), Italy

Search for more papers by this author

and

BENEDETTO PICCOLI

Istituto per le Applicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Roma, Italy

Search for more papers by this author

https://doi.org/10.1142/S0218202508003042Cited by:15 (Source: Crossref)

Abstract

Some models of flow on a network are discussed. Assuming a macroscopic approach on each arc of the network, we consider a system of conservation laws and various possible choices to describe the evolution at vertices are discussed. A general framework proposed in recent literature is presented, then some new solutions for the scalar case are proposed and analyzed.

Keywords:

AMSC: 90B20, 90B10, 35L65

References

D. Armbruster, P. Degond and C. Ringhofer, SIAM J. Appl. Math. 66, 896 (2006), DOI: 10.1137/040604625. Crossref, Web of Science, Google Scholar
M. K. Banda, M. Herty and A. Klar, Netw. Heterog. Media 1, 41 (2006). Crossref, Web of Science, Google Scholar
C. Bardos, A. Y. Le Roux and J. C. Nedelec, Comm. Partial Diff. Eqns. 4, 1017 (1979), DOI: 10.1080/03605307908820117. Crossref, Google Scholar
S. Benzoni-Gavage and R. M. Colombo, Euro. J. Appl. Math. 14, 587 (2003), DOI: 10.1017/S0956792503005266. Crossref, Web of Science, Google Scholar
A. Bressan , Hyperbolic Systems of Conservation Laws — The One-Dimensional Cauchy Problem ( Oxford Univ. Press , 2000 ) . Crossref, Google Scholar
Y. Chitour and B. Piccoli, Disc. Cont. Dyn. Syst. Ser. B 5, 599 (2005). Web of Science, Google Scholar
G. Coclite, M. Garavello and B. Piccoli, SIAM J. Math. Anal. 36, 1862 (2005), DOI: 10.1137/S0036141004402683. Crossref, Web of Science, Google Scholar
R. M. Colombo and M. Garavello, Netw. Heterog. Media 1, 495 (2006). Crossref, Web of Science, Google Scholar
C. Dafermos , Hyperbolic Conservation Laws in Continuum Physics ( Springer-Verlag , 1999 ) . Google Scholar
C. D'Apice and R. Manzo, Netw. Heterog. Media 1, 379 (2006). Crossref, Web of Science, Google Scholar
C. D'Apice, R. Manzo and B. Piccoli, SIAM J. Math. Anal. 38, 717 (2006). Crossref, Web of Science, Google Scholar
M. Garavello and B. Piccoli, Comm. Partial Diff. Eqns. 31, 243 (2006), DOI: 10.1080/03605300500358053. Crossref, Web of Science, Google Scholar
M. Garavello and B. Piccoli , Traffic Flow on Network ( Amer. Inst. Math. Sci. , 2006 ) . Google Scholar
M. Garavello and B. Piccoli, Commun. Math. Sci. 3, 261 (2005). Crossref, Web of Science, Google Scholar
S. Göttlich, M. Herty and A. Klar, Comm. Math. Sci. 4, 315 (2006). Crossref, Web of Science, Google Scholar
D. Helbing, J. Siegmeier and S. Lammer, Netw. Heterog. Media 2, 193 (2007). Crossref, Web of Science, Google Scholar
M. Herty, C. Kirchner and S. Moutari, Comm. Math. Sci. 4, 591 (2006). Crossref, Web of Science, Google Scholar
M. Herty, S. Moutari and M. Rascle, Netw. Heterog. Media 1, 275 (2006). Crossref, Web of Science, Google Scholar
H. Holden and N. Risebro, SIAM J. Math. Anal. 26, 999 (1995), DOI: 10.1137/S0036141093243289. Crossref, Web of Science, Google Scholar
J. P. Lebacque and M. M. Khoshyaran, Finite Volumes for Complex Applications II (Hermes Sci. Publ., 1999) pp. 551–558. Google Scholar
M. J. Lighthill and G. B. Whitham, Proc. Roy. Soc. London Ser. A 229, 317 (1955). Crossref, Web of Science, Google Scholar
A. Marigo and B. Piccoli, A fluid dynamic model for T-junctions, SIAM J. Math. Ann., in press . Google Scholar
P. I. Richards, Oper. Res. 4, 42 (1956), DOI: 10.1287/opre.4.1.42. Crossref, Web of Science, Google Scholar
D. Serre , Systems of Conservation Laws I and II ( Diderot Editeur , 1996 ) . Google Scholar